Parameters Estimation of a Proposed Non-Homogeneous Poisson Process and Estimation of the Reliability Function Using the Gompertz Process: A Comparative Analysis of Artificially Intelligent and Traditional Methods

Abstract

This work presents a novel approach to enhancing the rate of occurrence of non-homogeneous Poisson processes (NHPP) by utilizing the Gompertz distribution as the rate of occurrence. The primary objective of this study is to determine the parameters of the new process using both traditional methods and intelligent technology, specifically particle swarm optimization (PSO). Additionally, the study aims to estimate the reliability function of the process. The suggested model is simulated to achieve these goals, and the results are compared among various estimation techniques to identify the most accurate estimator. The study demonstrates that when predicting the time rate of occurrence of the proposed Gompertz process and its reliability function, the PSO algorithm outperforms other approaches. Furthermore, this research showcases a practical application utilizing real data from the Mosul power facility. Specifically, the data pertains to the stoppage times of two consecutive units of the Mosul Dam power stations from January 1st, 2021 to January 1st, 2022. Overall, this study introduces a novel process based on the Gompertz distribution to improve the rate of occurrence of NHPP. It employs particle swarm optimization to calculate the process parameters and estimate the reliability function. The superiority of the PSO algorithm is demonstrated through comprehensive comparisons. The practical application using data from the Mosul power facility further validates the effectiveness of the proposed approach.

Keywords

• Gompertz Process; Reliability function; Particle Swarm Optimization; Maximum Likelihood Estimation; Simulation.